RLC ckt's underdamped response

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SUMMARY

The discussion focuses on transforming the expression A cos(ωt) + B sin(ωt) into the form C cos(ωt + θ), specifically in the context of the underdamped response of an RLC circuit. It is established that this transformation is only valid when the amplitudes A and B are equal, leading to C being equal to 2A. In cases where A and B differ, the transformation cannot be achieved. The mention of phasors indicates a deeper exploration of complex numbers in circuit analysis.

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  • Understanding of RLC circuit dynamics and underdamped response
  • Familiarity with trigonometric identities and transformations
  • Basic knowledge of phasors in electrical engineering
  • Proficiency in complex number representation of sinusoidal functions
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barneygumble742
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hi...

how can i get A cos (omega t) + B sin (omega t)

into this form: C cos (omega t + theta) ?

does it equal to A+B cos (omega t - 90) ?

i know it has to do with the underdamped response of an RLC circuit. i
was looking into phasors as well.

any help would be greatly appreciated.

mark
 
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I do not think you can friend.
 
If A=B and C=2A, I think you can get it to work. But not in the general case where the amplitudes of the sin and cos components are different.
 

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